Hamilton described his Sunday in Zandvoort as "definitely frustrating for me" after he was unable to find a way past Mercedes' George Russell for third place in the closing laps.
The seven-time world champion's irritation peaked on team radio midway through the race when he caught up with team-mate Charles Leclerc.
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On fresher tyres after making a later pit stop than his team-mate, Hamilton initially pointed out as he arrived at the back of the sister Ferrari: "I'm quicker than Charles. These tyres are better."
However, Ferrari opted against reversing the order of the cars, which then led to an unusually-curt Hamilton barking: "We are just losing time!" Then, once Leclerc had pitted, Hamilton sarcastically returned to the radio to say: "A great way of wasting time guys, good job."
He went on to finish fourth on the tail of Russell, who had been instructed by Mercedes in the closing laps to let his team-mate Kimi Antonelli back by when the Italian caught the Briton on significantly faster and fresher tyres - decisive team tactics not lost on Hamilton.
Asked after the race about his blunt radio messages, Hamilton told F1: "I want to win. I want to win. I'm here to win.
"It is difficult when you are looking ahead and you see the two Mercedes drivers, they get the call and it's done, and they execute straight away.
"They let Kimi by and let him get on with the race. I was on a different strategy and it's not the same here.
"That's a little bit difficult but we'll take it offline and when I go back now, I'll speak to them about it."
'My goal is to try and lead this team to the championship'
Although Ferrari were outqualified by McLaren and Mercedes for both the sprint and main grand prix at Zandvoort, their longer-run pace was more impressive and they again became a factor in the podium hunt.
Hamilton, who had started fifth, praised the latest round of upgrades brought to the SF-26 for the first race after the summer break but expressed regret they had not been able to get a little more out of Sunday.
He told Sky Sports F1: "Firstly, the guys in the garage did a fantastic job. Pit stops, strategy was generally very, very good. The car felt awesome and they have continued to work so hard.
"We brought a bit of an upgrade here. We are just chipping away at it all the time. This first half of the season we have been losing three to five tenths on the straight depending on which track we go to and that's a hard deficit to overcome just through the corners. But we are close.
"But today was definitely frustrating for me.
"I'm here to win and I really believe that this team can win.
"We couldn't win this race but to win championships you have to pick up every point and the last few races have been difficult with penalties and stuff and then, today, I lost several seconds behind Charles which I think ultimately would have made the difference at the end.
"But we will take it offline. My goal is to try and lead this team to the championship and we've got some work to do for sure."
Finishing behind title leader Antonelli for the second day running, Hamilton left Zandvoort an increased 59 points off the Mercedes driver in the championship.
Formula 1 heads to Monza for Ferrari's home race at the Italian Grand Prix on September 4-6, live on Sky Sports F1. Stream Sky Sports with NOW - no contract, cancel anytime
